Conventionally, a connector is known which is configured by: a male connector including a male housing, and a male terminal that is inserted into and attached to the male housing; and a female connector including a female housing, and a female terminal that is inserted into and attached to the female housing, and in which the female connector has an elastic lance that is projected from the inner wall of the female housing, and that is engaged with the female terminal, the female terminal has: a tubular socket portion; an elastic-lance engagement hole that is disposed in a tubular wall portion of the socket portion; and an elastic contact piece that is disposed in the socket portion while only one end side is supported by the tubular wall portion of the socket portion, the female terminal is detachably fixed into the female housing by, in the elastic-lance engagement hole, engaging the elastic lance with the tubular wall portion of the socket portion, and, when the male connector and the female connector are fitted to each other, the male terminal is inserted into the socket portion of the female terminal, whereby the elastic contact piece is displaced to be contacted with the male terminal by means of a contact pressure, and an electrical connection between the male and female terminals is obtained (for example, see Patent Literature 1).